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Mixed metric dimension and exchange property of hexagonal nano-network [PDF]
Scientific ReportsThe mixed metric dimension of a graph is an important parameter in characterizing its structural complexity, specifically in nanoscale networks where precision is paramount.
Peide Liu +6 more
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Metric, edge-metric, mixed-metric, and fault-tolerant metric dimensions of geometric networks with potential applications [PDF]
Scientific ReportsResolvability parameters of graphs are widely applicable in fields like computer science, chemistry, and geography. Many of these parameters, such as the metric dimension, are computationally hard to determine. This paper focuses on Möbius-type geometric
Sakander Hayat +6 more
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On Mixed Metric Dimension of Rotationally Symmetric Graphs [PDF]
IEEE Access, 2020 A vertex u ∈ V(G) resolves (distinguish or recognize) two elements (vertices or edges) v, w ∈ E(G)UV(G) if dG(u, v) ≠ dG(u, w) . A subset Lm of vertices in a connected graph G is called a mixed metric generator for G if every two ...
Hassan Raza, Jia-Bao Liu, Shaojian Qu
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Mixed metric dimension over (edge) corona products
AKCE International Journal of Graphs and Combinatorics, 2023 A subset S of V(G) is called a mixed resolving set for G if, for every two distinct elements x and y of [Formula: see text], there exists [Formula: see text] such that [Formula: see text].
M. Korivand +2 more
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The mixed metric dimension of flower snarks and wheels [PDF]
Open Mathematics, 2021 New graph invariant, which is called a mixed metric dimension, has been recently introduced. In this paper, exact results of the mixed metric dimension on two special classes of graphs are found: flower snarks Jn{J}_{n} and wheels Wn{W}_{n}. It is proved
Danas Milica Milivojević
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Mixed metric dimension of hollow coronoid structure
Ain Shams Engineering Journal, 2023 Coronoid systems actually arrangements of hexagons into six sides of benzenoids. By nature, it is an organic chemical structure. Hollow coronoids are primitive and catacondensed coronoids. It is also known as polycyclic conjugated hydrocarbons.
Ali N.A. Koam +3 more
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On Mixed Metric Dimension of Some Path Related Graphs [PDF]
IEEE Access, 2020 A vertex $k\in V_{G}$ determined two elements (vertices or edges) $\ell,m \in V_{G}\cup E_{G}$ , if $d_{G}(k,\ell)\neq d_{G}(k,m)$ . A set $R_ {\text {m}}$ of vertices in a graph $G$ is a mixed metric generator for $G$ , if two distinct elements
Hassan Raza, Ying Ji, Shaojian Qu
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Graphs with mixed metric dimension three and related algorithms
AIMS Mathematics, 2023 Let $ G = (V, E) $ be a simple connected graph. A vertex $ x\in V(G) $ resolves the elements $ u, v\in E(G)\cup V(G) $ if $ d_G(x, u)\neq d_G(x, v) $.
Dalal Awadh Alrowaili +3 more
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Computing the Mixed Metric Dimension of a Generalized Petersen Graph P(n, 2) [PDF]
Frontiers in Physics, 2020 Let Γ = (V, E) be a connected graph. A vertex i ∈ V recognizes two elements (vertices or edges) j, k ∈ E ∩ V, if dΓ(i, j) ≠ dΓ(i, k). A set S of vertices in a connected graph Γ is a mixed metric generator for Γ if every two distinct elements (vertices or
Hassan Raza, Ying Ji
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Computation of mixed resolvability for a circular ladder and its unbounded nature. [PDF]
PLoS ONELet Γ = Γ(V ,E) be a simple, planar, connected, and undirected graph. The article primarily concentrates on a category of planar graphs, detailing the explicit identification of each member within this graph family. Within the domain of graph theory, the
Sunny Kumar Sharma +4 more
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